%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:43:39 PM UTC 2026
% Result : Theorem 8.90s 1.82s
% Output : Proof 8.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 83 ( 74 unt; 0 def)
% Number of atoms : 106 ( 64 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 15 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 128 ( 2 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_with_union) ).
fof(f1_nnf,plain,
! [B,C,D] :
( ( ( ~ intersect(B,D)
& ~ intersect(B,C) )
| intersect(B,union(C,D)) )
& ( intersect(B,D)
| intersect(B,C)
| ~ intersect(B,union(C,D)) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( ( ~ intersect(B,D)
& ~ intersect(B,C) )
| intersect(B,union(C,D)) )
& ( intersect(B,D)
| intersect(B,C)
| ~ intersect(B,union(C,D)) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( intersect(X0,X2)
| intersect(X0,X1)
| ~ intersect(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t29,plain,
ifeq(intersect(X1,union(X2,X3)),true,or(intersect(X1,X2),intersect(X1,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t56,plain,
ifeq(intersect(X1,union(X2,X3)),true,or(intersect(X1,X2),intersect(X1,X3)),true) = true,
inference(orient,[status(thm)],[t29]) ).
fof(f0,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f0_nnf,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t18,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t82,plain,
union(difference(X1,X2),difference(X2,X1)) = symmetric_difference(X1,X2),
inference(orient,[status(thm)],[t18]) ).
cnf(t84,plain,
true = ifeq(intersect(X1,symmetric_difference(X2,X3)),true,or(intersect(X1,difference(X2,X3)),intersect(X1,difference(X3,X2))),true),
inference(cp,[status(thm)],[t56,t82]) ).
cnf(t817,plain,
ifeq(intersect(X1,symmetric_difference(X2,X3)),true,or(intersect(X1,difference(X2,X3)),intersect(X1,difference(X3,X2))),true) = true,
inference(orient,[status(thm)],[t84]) ).
fof(f5,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f5_nnf,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c12,plain,
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t15,plain,
or(disjoint(X1,X2),intersect(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t61,plain,
or(disjoint(X1,X2),intersect(X1,X2)) = true,
inference(orient,[status(thm)],[t15]) ).
fof(f11,conjecture,
! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(f11_neg,negated_conjecture,
~ ! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [B,C] : ~ disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
~ disjoint(intersection(sk2,sk3),symmetric_difference(sk2,sk3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f11_nnf]) ).
cnf(c23,plain,
~ disjoint(intersection(sk2,sk3),symmetric_difference(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
disjoint(intersection(sk2,sk3),symmetric_difference(sk2,sk3)) = false,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t70,plain,
disjoint(intersection(sk2,sk3),symmetric_difference(sk2,sk3)) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t79,plain,
disjoint(intersection(sk2,sk3),symmetric_difference(sk2,sk3)) = false,
inference(rw,[status(thm)],[t70]) ).
fof(f7,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f7_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c14,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t8,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t76,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t918,plain,
disjoint(intersection(sk3,sk2),symmetric_difference(sk2,sk3)) = false,
inference(step,[status(thm)],[t79,t76]) ).
fof(f8,axiom,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(f8_nnf,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c15,plain,
symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t9,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t87,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t919,plain,
disjoint(intersection(sk3,sk2),symmetric_difference(sk3,sk2)) = false,
inference(step,[status(thm)],[t918,t87]) ).
cnf(t99,plain,
disjoint(intersection(sk3,sk2),symmetric_difference(sk3,sk2)) = false,
inference(orient,[status(thm)],[t919]) ).
cnf(t100,plain,
true = or(false,intersect(intersection(sk3,sk2),symmetric_difference(sk3,sk2))),
inference(cp,[status(thm)],[t61,t99]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t38,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t920,plain,
true = intersect(intersection(sk3,sk2),symmetric_difference(sk3,sk2)),
inference(step,[status(thm)],[t100,t38]) ).
cnf(t102,plain,
intersect(intersection(sk3,sk2),symmetric_difference(sk3,sk2)) = true,
inference(orient,[status(thm)],[t920]) ).
cnf(t824,plain,
true = ifeq(true,true,or(intersect(intersection(sk3,sk2),difference(sk3,sk2)),intersect(intersection(sk3,sk2),difference(sk2,sk3))),true),
inference(cp,[status(thm)],[t817,t102]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t998,plain,
true = or(intersect(intersection(sk3,sk2),difference(sk3,sk2)),intersect(intersection(sk3,sk2),difference(sk2,sk3))),
inference(step,[status(thm)],[t824,t34]) ).
cnf(t11,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t69,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(c11,plain,
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t17,plain,
or(not(disjoint(X1,X2)),not(intersect(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t62,plain,
or(not(disjoint(X1,X2)),not(intersect(X1,X2))) = true,
inference(orient,[status(thm)],[t17]) ).
fof(f2,axiom,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
fof(f2_nnf,plain,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
disjoint(intersection(X0,X1),difference(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t12,plain,
disjoint(intersection(X1,X2),difference(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t64,plain,
disjoint(intersection(X1,X2),difference(X1,X2)) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t77,plain,
true = disjoint(intersection(X1,X2),difference(X2,X1)),
inference(cp,[status(thm)],[t64,t76]) ).
cnf(t96,plain,
disjoint(intersection(X1,X2),difference(X2,X1)) = true,
inference(orient,[status(thm)],[t77]) ).
cnf(t97,plain,
true = or(not(true),not(intersect(intersection(X1,X2),difference(X2,X1)))),
inference(cp,[status(thm)],[t62,t96]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t74,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t922,plain,
true = or(false,not(intersect(intersection(X1,X2),difference(X2,X1)))),
inference(step,[status(thm)],[t97,t74]) ).
cnf(t923,plain,
true = not(intersect(intersection(X1,X2),difference(X2,X1))),
inference(step,[status(thm)],[t922,t38]) ).
cnf(t122,plain,
not(intersect(intersection(X1,X2),difference(X2,X1))) = true,
inference(orient,[status(thm)],[t923]) ).
cnf(t124,plain,
false = ifeq(true,true,intersect(intersection(X1,X2),difference(X2,X1)),false),
inference(cp,[status(thm)],[t69,t122]) ).
cnf(t924,plain,
false = intersect(intersection(X1,X2),difference(X2,X1)),
inference(step,[status(thm)],[t124,t34]) ).
cnf(t125,plain,
intersect(intersection(X1,X2),difference(X2,X1)) = false,
inference(orient,[status(thm)],[t924]) ).
cnf(t126,plain,
false = intersect(intersection(X1,X2),difference(X1,X2)),
inference(cp,[status(thm)],[t125,t76]) ).
cnf(t136,plain,
intersect(intersection(X1,X2),difference(X1,X2)) = false,
inference(orient,[status(thm)],[t126]) ).
cnf(t999,plain,
true = or(false,intersect(intersection(sk3,sk2),difference(sk2,sk3))),
inference(step,[status(thm)],[t998,t136]) ).
cnf(t1000,plain,
true = intersect(intersection(sk3,sk2),difference(sk2,sk3)),
inference(step,[status(thm)],[t999,t38]) ).
cnf(t1001,plain,
true = false,
inference(step,[status(thm)],[t1000,t125]) ).
cnf(t830,plain,
false = true,
inference(orient,[status(thm)],[t1001]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c11,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t830]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 11:30:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.90/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.90/1.82 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------